({\kappa},{\mu},\u{psion}=const.)-Contact Metric Manifolds With {\xi}(I_{M})=0

We give a local classification of ({\kappa},{\mu},\u{psion}=const.)-contact metric manifold (M,{\phi},{\xi},{\eta},g) with {\kappa}<1 which satisfies the condition" the Boeckx invariant function I_{M}=((1-({\mu}/2))/(\surd(1-{\kappa}))) is constant along the integral curves of the characteristic vector field {\xi}".